I am not an expert, but my understanding is that 'bhāvanā' basically means something like "causing to become or develop". In the context of spiritual practice it can mean something like "developing a mental state or mood", basically working with one's mind for a spiritual purpose, so, very similar to how 'meditation' and 'cultivation' are used in English now: http://en.wikipedia.org/wiki/BhavanaI don't know if 'abhāvanā' was ever actually used in India, but I think it makes good sense as a back translation from Tibetan. If the OP was not about the Tibetan term 'sgom med', then all bets are off.

The whole purpose of Buddhism is to have fun, isn't it? - Dzongsar Jamyang Khyentse Rinpoche

That's possible. Sanskrit words carry many meanings. Sanskrit is so highly inflected a word could be an inflection of a word that is an inflection of a completely different word. Know what I mean? And when words are adopted into another language, the meaning and usage can change. Context is important.

Worthy, wise and virtuous: Who is energetic and not indolent, in misfortune unshaken, flawless in manner and intelligent, such one will honor gain. - Digha Nikaya III 273

Don't forget that a long or short vowel can change a word too. Hara is a name for Shiva, but Harā is a name for Radhā. Hare is either the vocative of Hari or the vocative of Harā. That's why Sanskrit lends itself to poetry and word play so well.

Worthy, wise and virtuous: Who is energetic and not indolent, in misfortune unshaken, flawless in manner and intelligent, such one will honor gain. - Digha Nikaya III 273

Cologne Sanskrit Digital Lexicon uses an adapted version of Harvard Kyoto Convention for transliteration of sanskrit.Thus A signifies a long vowel a,ie aa. Translation of aadhyaana or AdhyAna is correct.

There is the Digital Sanskrit Buddhist Canon, where you can search; adhyana gave no results, there are results for mahamudra.

If you're looking for the Mahamudra term 'nonmeditation', then I'd say Dzogchungpa has it right, as abhAvanA would be the closest you can get to sgom med. DhyAna is the Sanskrit equivalent of the term bsam gtan, not sgom, so if you're looking for sgom med, then it wouldn't be adhyAna. However, abhAvanA isn't in the Mahavyutpatti, so you're probably not going to find a standard term that was translated from Sanskrit into Tibetan for nonmeditation. At least not in any dictionary.

True, 'na' is indeed a negation... astika/nastika; asmi/nasmi (I am, I am not). But so is 'a'. Iirc it's sandhi that determines which is used. Moreover, Vedic Sanskrit and Classical Sanskrit are quite different in some areas. Just some more info.

Worthy, wise and virtuous: Who is energetic and not indolent, in misfortune unshaken, flawless in manner and intelligent, such one will honor gain. - Digha Nikaya III 273

Beyond these three upayas, shambhavopaya, shaktopaya, and anavopaya, there is another upaya. Although it is not actually an upaya, yet it is mentioned in Kashmir Shaivism. This upaya is called anupaya. The word anupaya means “no upaya.” Thoughtlessness is called shambhavopaya. One-pointedness is called shaktopaya. Concentration on and with the support of mantra and breathing and all other elements is called anavopaya. Above all of these is anupaya. In anupaya, the aspirant has only to observe that nothing is to be done. Be as you are. If you are talking, go on talking. If you are sitting, go on sitting. Do not do anything, only reside in your being. This is the nature of anupaya. Anupaya is attributed to ananda shakti of Shiva and is called anandopaya.

The whole purpose of Buddhism is to have fun, isn't it? - Dzongsar Jamyang Khyentse Rinpoche

Quite possibly there is no actual word for such a thing. Or, it may not be a word, but a phrase. Unless one can be sure that this originally comes from an actual Sanskrit source. Otherwise you may just be creating a neologism. Not necessarily a bad thing, but needs to be acknowledged for what it is.